I was a LMDE (Mate) user until it was discontinued, now I use the Ubuntu branch of LM (Cinnamon and Xfce). Yesterday I installed LMDE 2 Mate 32 bit on an old (core 2 duo 2GB RAM) PC and I liked it! So fast and responsive! In my humble opinion this is the leanest version of Mint available now, it idles at just 180 MB RAM usage (after some minor tweaking). The kernel is old but this is better for old hardware.
Very nice! Perfect for old/weak PCs.
So, in the end, it isn't really necessary to distrohopping to find an ultra-light distro, Mint family has one and it works very well.

update:

The only limitations I've found in LMDE 2 Mate are:
1 - the slightly longer boot time (compared to the main LM branch)
2 - the management of repos (more complicated) and the lack of PPAs
3 - the less customizable Mate desktop (compared to Xfce; but Caja is better than Thunar)
4 - some minor bugs like the theme selector.

Yes it's good, I'd prefer LMDE2 hands down for old and weak machines, it's noticeably faster/more responsive. About the "bugs", I've found that are not, really bugs, theme selector works OK. And about Mate, well... it's a matter of taste. I still prefer Xfce, but also Mate is good, the only real limitation is the panel, inferior to the Xfce panel because is less customizable. Imho Caja is a better file manager than Thunar, but it's just my preference. Mate and Xfce have approximately the same impact on system resources, both are lightweight and fast.

ilikereading wrote:For example, Libre office or wine or vlc player. Are they working the same or even better? Have the same level of security or stability?

LibreOffice and any other program works exactly as in the Ubuntu branch of LM. But LMDE2 is overall lighter, so there is more room for programs, if the RAM is tight.
LMDE2 32bit can run comfortaby LibreOffice, Firefox and some other common programs (even GIMP) with just 1GB RAM.

Stability is a prime concern in Debian and, by bloodline, LMDE; some have complained that both sets of devs sacrifice too much for it. I don't like to have to fiddle constantly with my daily driver, I want to sit down and have it work once I've customized it the way I like it. LMDE2 does that for me.

Security is what you make it on any system. I tend to be a bit lax myself, but you can up security measures to suit whatever level of paranoia suits you.

3 - the less customizable Mate desktop (compared to Xfce; but Caja is better than Thunar)

I'm interested in knowing what is less customizable as I find just the opposite.

The only thing about LMDE that bothers me is application version numbers lagging behind Mint. I've noticed this with QupZilla and Conky, I imagine there are others.

Mike

Basically the Mate panel. Is very difficult to change the font, the font size and its color. If you have a solution, please let me know. As far as I understand, the old trick of creating a .gtkrc-2.0 file is no working anymore with gtk3. Yes, maybe there are workarounds: https://github.com/mate-desktop/mate-panel/issues/507
but there are not straightforward, intuitive and user friendly, in my humble opinion.
The Xfce panel is more customizable and in a very easy way. Changing simple things like fonts and colors in a "main" DE should be just a matter of few clicks.

In short, you have to create a gtk.css file in /home/config/gtk-3.0/ This file will control the behaviour of gtk3 elements in the system. I have to find out how to change not only the panel "normal" color background but also the color background of the active and selected elements.
From the link above, I managed to change the clock/date color, but I have no idea how to change the other elements. If I can find a solution for this, I will move from Xfce to Mate, because indeed Mate has some better components (I prefer Caja over Thunar) and looks more polished out of the box.